Progressive reading and intermediate distance lens defined by employment of a zernike expansion

ABSTRACT

There is provided a lens that includes a corridor having a width greater than or equal to about 6 millimeters. The lens has astigmatism less than or equal to about 0.5 diopter within the corridor. There is also provided an item of eyewear that includes such a lens, and a method for representing a surface of an ophthalmic lens.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to ophthalmic lenses and moreparticularly, to ophthalmic lenses for the compensation of presbyopia.

2. Description of the Prior Art

Presbyopia is a condition characterized by a reduction in a person'sability to focus upon nearby objects, i.e., accommodation. The onset ofpresbyopia normally occurs at around the age of forty, even in thosepeople having otherwise good health and normal vision. The conditionmakes near-distance activities, such as reading, typing, and so on moredifficult, or even impossible in advanced cases. Close work may beaccomplished more comfortably, in most cases, by utilizing simplesingle-vision positive lenses having a refractive power of one to threediopters. For many years, this refractive power has been “added” to theprescriptions of people having other refractive deficiencies, e.g.,myopia, astigmatism, etc., in the form of “bifocals,” or, whenaccommodation is severely limited, “trifocals”.

An annoying demarcation between the distance and reading portions ofthese lenses led to development of “blended” lenses. The distance andreading portions of the lenses are artificially obliterated, butnonetheless remain in a form that interferes with a comfortable transferfrom distance to reading portions.

A true multifocal lens has a property such that the refractive powervaries continuously and monotonically from top to bottom. While aperceived image quality, i.e., acuity, may vary considerably with adirection of view, i.e., horizontal look angle, some useful imagequality is available in most areas of the lens. This type of lens hasbecome known as a “progressive addition” lens (PAL), or “progressivemultifocal”, “a lens designed to provide correction for more than oneviewing distance in which the power changes continuously rather thandiscretely” (ANSI Z80.1-1999 for Ophthalmics—Prescription Ophthalmiclenses—Recommendations). Many such designs possess a di-polar character,possessing two identifiable areas intended for distance viewing andreading, which are normally connected by a narrow corridor of reasonablygood image quality, where power of the lens varies from that requiredfor reading to the distance prescription.

One such design is described by U.S. Pat. No. 5,123,725 to Winthrop,entitled “Progression Addition Spectacle Lens”. A lens design havingsimilar characteristics is documented in U.S. Pat. No. 5,048,945 to Uenoet. al., entitled “Progressive Power Lens”. Although these lenses appearto function in a similar fashion, the derivation of the shape for theiractive surface is quite different from one another. Likewise for U.S.Pat. No. 4,988,182 to Takahashi.

Multifocal lenses typically achieve their performance by generalizingthe well-known bifocal, or trifocal lenses to include a multiplicity ofcontinuous zones of varying refractive power. This is accomplished bymaking one of the lens surfaces a non-spherical, i.e., aspheric, shape.In most cases, this aspheric surface is mathematically modeled so thatits contours may be manipulated and, finally described with greataccuracy for manufacturing purposes. Thus, many modern progressive lensdesigns are based on an application of differential geometry, and someincorporate methods of variational calculus, or a graphical equivalent,to derive progressive surfaces necessary to obtain a desired refractivepower distribution that will satisfy functional requirements andboundary conditions. See O. N. Stavroudis, “The Optics of Rays,Wavefronts and Caustics”, Academic Press, 1972.

The differential geometry representation of PAL surfaces providesincomplete information, with the possibility of misleading an analystabout image quality. The surfaces that result from the application ofthese design techniques may indeed produce power distributions that aresought, albeit in a narrow vertical corridor, but the visual acuity isoften compromised by attempts to expand the power range, or to compressit into too short a vertical corridor. The result is that good visionmay be obtained only in discrete areas targeted for distance and nearviewing, with the remainder of the corridor, and most areas outside thecorridor, delivering only marginal image quality.

A mean local curvature of the aspheric surface of the lens may becontrolled, within limits imposed by the power distribution requirementsand aberration constraints, to achieve a desired variation in diopterpower. Aberration content of a progressive addition lens is ordinarilycharacterized by evaluating a difference in principal curvatures ingeodesic orientations at selected points on the lens, and isconventionally expressed solely as astigmatism.

An assumption that the aberration content is pure astigmatism is, ofcourse, a simplistic one. If ray pencils are small, the approximationmay be fairly good. If the ray pencils pass into a fully dark-adaptedeye, many different aberration components may be present, and it is asummation of these that will determine the ultimate visual acuity whenviewing through different sections of the lens.

The characterization of any PAL reduces, naturally, to some physicalsurface shape. This shape should ideally be continuous, monotonic, andfree of severe second and third partial derivatives, otherwise the userwill be acutely aware of local variations in both geometric distortionand acuity, and will experience discomfort in extended use. Theselimitations restrict the power distributions that may be implemented inpractice. If the local power of a PAL is required to change rapidly frompoint to point, severe inflections in the aspheric surface will bepresent, and the stigmatism of the transmitted ray pencil will be lessthan ideal in some portions of the lens.

Another aspect of the surface characterization problem is that any suchsurface must be accurately modeled mathematically in order to begenerated and manufactured. Many mathematical representations have beenapplied to the characterization of PAL surfaces. Most of these have beenCartesian-based, that is, expressed in X-Y coordinates. This is notnecessarily bad, but since the eye pupil is a circular aperture, itmakes some sense to fit a function to the PAL surface that is based uponpolar coordinate geometry. As in many other situations requiringmathematical analysis, matters are made easier by choosing a coordinatesystem matched to the physical circumstances.

People normally perform reading tasks in a large variety of head andbody positions. While certain texts describe “ideal” body geometry forfatigue-free reading, this is rarely realized in practice. Compromisesmade to achieve a desired power distribution, coupled with a need toaccommodate the physiological act of convergence of the two separatevisual systems when reading, often results in a need for the user toretrain himself to substitute head movement, when using PALs, for themore natural act of eye movement. Further, variations over a user baseof interpupillary distance, center-of-rotation, and other facialcharacteristics, require that each prescription be custom fitted withgreat care. These “fitting factors” limit the scope of application andthe overall utility of these designs. A design that is not constrainedby these fitting factors will find more widespread application, and willbe easier to accept in use.

SUMMARY OF THE INVENTION

There is a need for a progressive addition lens with continuousmonotonic change of powers, with no zone of stable power, tailored toprovide high visual acuity for users involved in reading and in viewingat near and intermediate distances up to about four meters. The lens, ora pair of such lenses, can be situated in a lens holder, for example, aframe or rim for a pair of glasses or holder for a pair of rimlessglasses.

There is also a need for such a lens with smooth gradual uninterruptedchange of powers that may be worn and used comfortably and effectivelywithout a need for custom fitting, and that contains the powers in awide corridor that allows its user to function without excess headmovement in order to keep viewed objects constrained within a narrowcorridor of high acuity.

There is described herein a lens that includes a corridor , i.e., zoneof high acuity viewing incorporating near and intermediate distances,having a width greater than or equal to about 6 millimeters along itslength. The lens exhibits astigmatism less than or equal to about 0.5diopter within the corridor and a linear progression of power changesbetween the top and bottom of the corridor.

There is described herein a lens that includes a corridor, i.e., zone ofhigh acuity viewing incorporating near and intermediate distances,having a width greater than or equal to about 10 millimeters along itslength. The lens exhibits a refracted root-mean-square (RMS) angularblur radius less than or equal to about 0.0005 radians within thecorridor and power progresses linearly between the top and bottom of thecorridor.

There is also described herein an item of eyewear. The item of eyewearincludes a pair of progressive addition lenses situated in a lens holderto satisfy a span of interpupillary distances of at least 6 millimeters.

A method described herein includes using a Zernike expansion torepresent a surface of an ophthalmic lens.

Another method described herein includes using a Zernike expansion torepresent a surface for each of a pair of progressive addition asphericlenses, and situating the pair of lenses in a lens holder to satisfy aspan of interpupillary distances of at least 6 millimeters.

Another method described herein includes designing an ophthalmic lens,where the designing employs, as a design parameter, a pupil size of awearer under conditions of use of the ophthalmic lens.

Another method described herein includes designing an ophthalmic lens,where the designing employs, as design parameters, (a) a predeterminedboundary shape of the ophthalmic lens for ultimate use, and (b) apredetermined boundary size of the ophthalmic lens for ultimate use.

An embodiment of a lens produced by the methods described herein is aprogressive addition lens having a continuous monotonic change of powersat an average rate less than or equal to 0.1 diopter per millimeter fromreading at a distance of about 35 centimeters (cm) to about 45 cm fromthe lens to viewing at near and intermediate distances, from about 50 cmto about four meters from the lens. The powers are within a corridorhaving a width greater than or equal to about 6 millimeters along itslength, wherein the lens has surface astigmatism less than or equal toabout 0.5 diopter within the corridor. The corridor expands to a widthgreater than or equal to about 15 millimeters along its length whereinthe lens exhibits astigmatism less than or equal to about 1.0 diopterwithin the corridor.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a topological plot of the contours of the aspheric surface ofa 2.0 diopter lens.

FIG. 2 is a contour plot of the sag differences between the sphericalsurface and the aspheric deformations.

FIG. 3 is a plot depicting the local thickness values for a 2.0 diopterlens.

FIG. 4 is a three-dimensional depiction of the edge thickness values fora 2.0 diopter PAL lens.

FIG. 5 is a graphic depicting incremental surface power contourintervals present in the aspheric surface of a 2.0 diopter lens, basedupon differential geometry calculations.

FIG. 6 is a graphic depicting the distribution of contour intervals ofrefractive power in a 2.0 diopter example of a PAL, based upon raytracecalculations.

FIG. 7 is a graphic depicting the rate of progression of refracted powerin the surface of a 2.0 diopter lens.

FIG. 8 depicts local incremental astigmatism contour intervals (e.g.,0.5 diopter) based upon a difference in principal surface curvatures ina 2.0 diopter lens.

FIG. 9 is a topographic map of image quality throughout a 2.0 diopterlens, depicting contour intervals of refracted RMS angular blur radiusexpressed in radians (e.g., 0.0005 radians), based upon actual raytracecalculations.

FIG. 10 is a plot of the 0.5 diopter incremental astigmatic contourinterval of FIG. 8 superposed upon the incremental surface power contourintervals of FIG. 5.

FIG. 11 is a plot created by superposing the 0.0005 radian blur contourinterval from FIG. 9 upon the raytrace-based refracted power contourintervals of FIG. 6.

FIG. 12 is an illustration of an item of eyewear that includes a pair oflenses designed and manufactured in accordance with the presentinvention.

NOTE: The term “incremental” in the description of FIG. 5, FIG. 8 andFIG. 10 refers to the respective component of the surface model that isadded to the spherical surface.

DESCRIPTION OF THE INVENTION

The present invention pertains to compensation of presbyopia. Anophthalmic lens is a lens used for correcting or measuring refractiveerrors of the eye and/or compensating for ocular muscle imbalances (DCline, H. W. Hofstetter, J. R. Griffin, Dictionary of Visual Sciences,Third Edition, Chilton Book Company, 1980). There is described herein alens that is non-spherical, i.e., aspheric, and non-symmetrical about awide corridor of high-acuity. The non-symmetry permits the lens to bebetter adapted to applications in which no custom fitting operations areperformed. Thus, variations in personal facial geometry, and normalconvergence of the optical paths, as a user accommodates fromintermediate to near objects, may be dealt with more effectively.

Enlarging the field of view, and/or the pupil diameter, of an opticalsystem increases the difficulty of achieving a given level of imagequality. Correspondingly, increasing the area of an ophthalmic lensmeans that a required level of image quality must be achieved over agreater range of input parameters. Since there are only a fixed numberof variable parameters to optimize, it stands to reason that requiringthis fixed number of variable parameters to address image quality issuesover a larger area will result in diminished acuity performance.Reducing the area of the optimization from that of an oversized blank tothe specific area of the glazed lens element permits a designer toimprove correction with a fixed number of design degrees of freedom.Thus, designing a lens to a specific shape and size will result inimproved vision correction properties of the lens.

An aspheric prescription is a formula that includes all parametricinformation required to model the aspheric surface mathematically andphysically. The lens described herein is tailored for use with aspecific, preconceived lens boundary shape and size. That is, itsaspheric surface geometry is optimized taking into account a finalboundary contour. The aspheric prescription is not contrived for anoversized blank intended to be edged to one of several possible smallercontours, since this would require that the aspheric profile be a“compromise” shape, which in turn reduces overall imagery performance.

The lens is conceived for implementation as a stand-alone optical aid,suitable for use without providing for individual correction for visualdefects. This utility is accomplished by abandoning a conventionalrequirement to view the most distant subject material, and therebyprovide more flexibility in operation, because a usable field-of-viewmay be made considerably wider than in conventional, full rangemultifocal progressive lenses intended for general-purpose application.

The lens is intended for use as an aid to those who possess good vision,but for whom age has limited the range of focal accommodation, e.g.,those afflicted with presbyopia. It is also intended to be forgiving ofthe precision required in fitting conventional progressive multifocallenses, whose corridor, i.e., zone of high-acuity viewing, may be quitenarrow. While the lens design principles described herein couldconceivably be incorporated into conventional prescription lenses, theyprovide considerable value as an aid to normal vision.

A viewing distance, in the context of lens design, is typicallycategorized as being one of a near distance, i.e., reading distance, anintermediate distance, or a far distance, i.e., beyond 6 meters. Thelens described herein is a multifocal ophthalmic lens optimized forviewing objects from distances of approximately 40 centimeters, i.e.,reading distance, up to about four meters.

Such a lens is created by utilizing a mathematical formula, i.e., aZernike polynomial expansion, not commonly encountered in the ophthalmicfield. When fitting polynomial expansion functions to arrays of points,i.e., surface coordinates, complex, high-order functions may often bemade to fit better than simple ones, but smoothness may suffer, andperformance with it. As described herein, a set of Zernike polynomialsis employed to define the surface characteristics of the lenses. Below,there is presented a description of a method for determining a surfacecharacteristic of a lens, and a description of an embodiment of such alens.

Ophthalmic lens quality is conventionally evaluated and compared using a5 millimeter (mm) diameter pupil. This diameter, though relativelysmall, is sufficient to render the astigmatic approximation inadequatein some cases. It is not unusual to discover that an astigmatism-basedevaluation of imagery performance differs by as much as a factor of twofrom measured visual acuity. Reducing the pupil diameter used in thisevaluation to perhaps 3.5 mm reduces this discrepancy. This diametercorresponds more closely to that which is present under illuminationconditions normally deemed adequate for comfortable reading.

An aberration function is a method for modeling the aberration contentin an optical system. Raytrace information is generated by tracing raysthrough an optical system, enabling the analyst to construct amathematical model of the aberration content, i.e., the aberrationfunction, of an optical system. Assuming the existence of a 3.5 mmdiameter pupil near the center of rotation of the eyeball, an imagequality function is constructed having a root sum square (rss) value,enabling the evaluation and quantification of the aberration function,including judiciously-chosen weighting factors, to be used as an acuitymetric for the entire lens. The weighting factors are weights assignedto components of the image quality function, in order to insure that themathematics relate to the physical performance. The acuity metric is amethod of correlating the modeled aberration function with its impactupon acuity.

In optimization, acuity metric targets are assigned to diopter powervalues at locations in the lens that correspond to a desired horizontaland vertical power distribution. Targets are not assigned to those areasthat would fall outside the boundary of the lens that would be glazedinto a frame containing the lens. To design a PAL as described herein,one would likely employ a computer program to adjust the variables tocompel the power across a horizontal strip of the lens to have someconstant value, say 1.4 diopter. A different horizontal strip might beassigned different targets, say 0.9 diopter.

Chromatic aberration components, variations of focus or magnificationthat are color dependent, are ignored, since a single element has nousable variables with which to deal with these image defects. Likewise,geometric distortion, a field-dependent variation in magnification, isnot made part of the imagery metric, since this image defect isimplicit, to some extent, in any progressive reader, and isnon-orthogonal to image defects that affect visual acuity.

The coefficients of a Zernike expansion are employed as designvariables, assuming a spherical, i.e., parent curve on the front surfaceof the lens. The Zernike expansion, or polynomial set, is a fairlycomplex mathematical formalism. It is a transcendental function havingan unlimited number of terms and coefficients. A comprehensiveexplanation of the construction and application of Zernike polynomialsis provided in a pair of volumes of a set titled “Applied Optics andOptical Engineering”, edited by Robert R. Shannon and James C. Wyant,Academic Press, Inc. (hereinafter “Shannon and Wyant”). Volume X, pp.193 -221, discusses theory and applications with much graphical support.In Volume XI, pp. 201 - 238, this theory is connected to image qualityinterpretations based upon geometrical optics concepts.

The Zernike polynomial employed to model a progressive aspheric surfacemodifies a basic parent spherical convex front surface. This frontsurface, as above, may be viewed as having a “sag” function, whichrepresents a departure from flatness, expressed in terms of radial andazimuthal coordinates, referenced to an expansion axis. The total “sag”Z_(T) of the progressive aspheric surface at any point in the polarcoordinate system is the summation of the spherical component Z_(S) andthe Zernike component Z_(Z):

Z _(T) =Z _(S) −Z _(Z)  . (1)

The spherical component Z_(S) of the sag of the surface is given by:

Z _(S) =cR ² /[1+(1−c ² R ²)¹/²],   (2)

where c is the reciprocal of the base surface radius of curvature, and Ris the normalized zonal radius.

FIGS. 1-11 depict various characteristics of a lens, generallydesignated by reference numeral 100. Lens 100 is a left eye lens. Thatis, a person wearing lens 100 would wear it in front of their left eye.FIGS. 1-3, 5, 6, and 8-11 are views from the perspective of a personfacing the wearer, such that the nose of the person wearing lens 100would be at the lower left side of the figures. In FIG. 4, the nose ofthe wearer of lens 100 would be at the lower front left corner of thefigure.

FIG. 1 is a topological plot of the contours of an aspheric surface oflens 100. The sagittal values, i.e., sags, of the surface are depictedwith respect to the highest point on the surface. In FIG. 1, the saglocation is indicated as point 110. Point 110, which is an arbitrarypoint, designated (R, φ), comprises the coordinate location forevaluation of the Zernike expansion for derivation of the sag value.

The Zernike component Z_(Z) is the fairly lengthy summation, anexemplary form of which is provided below:

Z _(Z) =C ₁₁ RCosφ+D ₁₁ RSinφ+C ₂₀(2R ²−1)+C ₂₂ R ²Cos(2φ)+

D ₂₂ R ²Sin(2φ)+C ₃₁(3R ²−2)RCos(φ)+D ₃₁(3R ²−2)RSin(φ)+

C ₄₀(6R ⁴−6R ²+1)+C ₃₃ R ³Cos(3φ)+D ₃₃ R ³Sin(3φ)+

C ₄₂(4R ²−3)R ²Cos(2φ)+D ₄₂(4r ²−3)R ²Sin(2φ)+

C ₅₁(10R ⁴−12R ²+3)RCos(φ)+D ₅₁(10R ⁴−12 R ²+3)RSin (φ)+

C ₆₀(20R ⁶−30 R ⁴+12R ²−1)+C ₄₄ R ⁴Cos(4φ)+D ₄₄ R ⁴Sin(4φ)+

C ₅₃(5R ²−4)R ³Cos(3φ)+D ₅₃(5R ²−4)R ³Sin(3φ)+

C ₆₂(15R ⁴−20R ²+6)R ²Cos(2φ+D ₆₂(15R ⁴−20R ²+6)R ² Sin(2φ)+

C ₇₁(35R ⁶−60R ⁴+30R ²−4)RCos(φ)+

D ₇₁ (35R ⁶−60R ⁴+30R ²−4)RSin(φ)+

C ₈₀(70R ⁸−140R ⁶+90R ⁴−20R ²+1)+

C ₅₅ R ⁵Cos(5φ)+D ₅₅ R ⁵Sin(5φ)+C ₆₄(6R ²−5)R ⁴Cos(4φ)−

D ₆₄(6R ²−5)R ⁴Sin(4φ)+C ₇₃(21R ⁴−30R ²+10)R ³Cos(3y)−

D ₇₃(21R ⁴−30R ²+10)R ³Sin(3φ)+

C ₈₂(56R ⁶−105R ⁴+60R ²−10)R ²Cos(2φ)+

D ₈₂(56R ⁶ −105R ⁴ +60R ²−10)R ²Sin(2φ)+

C ₉₁(126R ⁸−280R ⁶+210R ⁴−60R ²+5)RCos(φ)+

D₉₁(126R ⁸−280R ⁶+210R ⁴−60R ²+5)RSin(φ).   (3)

This particular interpretation of the Zernike expansion is truncatedwith term number thirty-four. Carrying additional terms might, or mightnot improve accuracy, depending upon the specific circumstances. Usingmore terms in the expansion might, for example, be beneficial when thereading power (in diopters) is quite high.

Additive power is determined in the front, convex, surface of the lensby adding and subtracting Zernike terms to provide for a polynomialdeformation of that surface. Following a convention for Zernike termsdescribed in Shannon and Wyant, a non-spherical deformation of the frontsurface of the lens is determined by adding, algebraically, thesummation of the Zernike terms with the constants listed below. TheZernike coefficients below having been computed for a radiusnormalization value of 50 mm.

C₁₁=−1.425304

D₁₁=1.028192

C₂₀=0.136984

C₂₂=0.039202

D₂₂=0.924985

C₃₁=−0.755616

D₃₁=−1.910942

C₄₀=1.047668

C₃₃=0.421116

D₃₃=−0.096886

C₄₂=−0.527587

D₄₂=0.629941

C₅₁=−0.332642

C₅₁=−0.797667

C₆₀=0.034681

C₄₄=−0.000530

D₄₄=−0.015176

C₅₃=0.377007

D₅₃=−0.084890

C₆₂=−0.294204

D₆₂=0.254671

C₇₁=−0.159434

D₇₁=−0.021080

C₈₀=−0.038708

C₅₅=0.072358

D₅₅=−0.096909

C₆₄=−0.039248

D₆₄=−0.106494

C₇₃=0.084212

D₇₃=0.091244

C₈₂=−0.044443

D₈₂=0.059156

C₉₁=−0.037741

D₉₁=0.017304

The merit function, i.e., image quality function, for the lens isoptimized using a modified least-squares path-of-steepest-decenttechnique, with adjustments made several times to the image qualityfunction construction as the lens approaches its desired performance.For an explanation of the “merit function” composition, see: Smith,Warren J., “Modern Lens Design”, McGraw-Hill, 1992, or Laikin, Milton,“Lens Design”,n2 E CI Marcel-Decker, 1995. Adjustments are made to theZernike coefficients in order to optimize both the distribution ofdiopter power and the image quality. The process of lens optimizationis, in general, well known to experts in the field. See Smith or Laikinabove.

The PAL concept and design optimization approach described above areapplicable to a wide range of applications and requirements. The conceptdescribed herein, utilizing a Zernike polynomial model of theprogressive aspheric surface, might well be applied to a lensconfiguration of any peripheral dimensions, and might well be utilizedto create a wide range of maximum/minimum power over an arbitrarycorridor length. In particular, although the figures depict theproperties of a specific lens shape, having a maximum power zone of 2.0diopter, a different peripheral lens shape might be addressed, or thedesign modified to create a different maximum power, say 1.5 diopters.The deterministic optimization procedure described above, and thediopter power distribution, may be varied within rather wide limits, say0.25 to 4.0 diopters, to produce an assortment of designs forcompensation of varying amounts of presbyopia. An approach, utilizingactual raytrace information to model image quality, is preferable to theuse of differential geometry to model surface shapes, which only infersimage quality.

There are, of course, many possible methods that might be used fordefining an optical surface shape. The Zernike expansion, it wasdecided, is appropriate to this application. However, Legendrepolynomials might have worked as well. In either case, the contour ofthe aspheric surface is evaluated at any selected point inradial/azimuthal coordinates to derive the topology. The opposite sideof the lens is a simple spherical surface. In an exemplary embodiment,its radius is 101 mm.

FIG. 5 is a contour interval-style diagram depicting the incrementalsurface power of lens 100 and the local power present in the asphericsurface of lens 100, based upon differential geometry calculations. Lens100 has power of approximately 2.0 diopter in a reading zone 120.

A major reference point (MRP) is used, in optometric fitting, to locatea lens blank with respect to a fitting to a patient, and to a templateused to create a lens peripheral shape from a blank. Referring to FIG.5, an MRP 140 is utilized for establishing a location of lens 100 in aframe (see FIG. 11). The reading power is present at reading zone 120approximately 18 mm below MRP 140, which is in turn located 2 mm above ageometric center 160 of the Zernike expansion function. That is, MRP 140is located 2 mm above the coordinate center (geometric center) of theZernike expansion. The power halfway between MRP 140 and reading zone120 is approximately 1.6 diopters. In the upper portion of the lens, thedioptric power diminishes to about 0.20 diopter at a vertical distanceof 10 mm above MRP 140.

Normally, in prescription ophthalmic optics, the actual “lens” is aportion of a large (70-75 mm) circular blank. Once the patient selects aframe, facial factors are measured (interpupillary distance, bridgeheight, etc.), and the lens is “fitted” for edging. As explained below,lens 100 is designed for a specific frame configuration, and thus, doesnot require the conventional fitting process to be applied.

Lens 100 has a generic peripheral shape, and, for the exemplaryembodiment in FIG. 5, a width dimension of about 58 mm, and a height ofapproximately 46 mm. Specifically, its width might range from 45 to 65mm, and the height from 30 to 55 mm. In this configuration, certainsubtle fitting considerations, e.g., alignment marks and positionindicators, normally included in the glazing of prescription progressiveeyewear have been omitted. Consequently, considerations such asnear-point convergence angle, pantascopic tilt, and prism thinning havebeen included in lens 100, and will have correct values, despite thefact that lens 100 will not be edged in conventional fashion.

Although lens 100 is described in FIG. 5 as having power ofapproximately 2.0 diopter in reading zone 120, it may be made suitable,by modifying the Zernike coefficients, for applications having as muchas 4 diopter reading power, or as little as 0.25 diopter.

FIG. 2 is a contour interval-style plot of the front sag difference,subtracting the best fitting sphere of lens 100. That is, it shows acontour plot of the sag differences between the spherical surface andthe aspheric deformations. Note the deformations have no axial orbilateral symmetry. FIG. 2 depicts contour intervals of asphericdepartures from a best fitting spherical radius. In general, it will bepossible to begin with some spherical surface, and then remove material,so that a desired aspheric surface is the result. Also, in general, thematerial to be removed may be minimized by beginning with a “best fitsphere” having a proper radius. While the aspheric surface may notactually be created by material removal, the concept is useful indescribing the various characteristics of the aspheric surface.

FIG. 3 is a contour interval-style plot of the thickness of lens 100.FIG. 3 illustrates variation in thickness for various locations in lens100. Note that the thickness values vary from about 2.0 mm near thecenter, and from 1.7 to about 1.0 m around the edge. In order to fitproperly in a frame, and in order to possess sufficient thickness forsafety purposes, the thickness of lens 100 must be adequate at allpoints on its periphery, and in its central zones. Since local thicknessis related to the Zernike coefficients, it may be seen that local powervariations will be accompanied by thickness variations in the lens.Greatest thickness values are in a region 200 near an eye pupillocation, i.e., straight-ahead gaze, and the thickness tapers to valuesbetween 1.8 mm and 1.1 mm elsewhere.

FIG. 4 is a perspective-style diagram depicting peripheral edgethickness of lens 100. For clarity, only edge thickness values areshown.

Referring again to FIG. 5, there is shown incremental power distributionfor lens 100 computed from an average of local principal curvatures(differential geometry). Heavy lines represent 0.5 diopter intervals.Thin lines represent 0.25 diopter intervals. Contours of constant (mean)power zones 180 are generally evenly spaced and not preciselyhorizontal, but slightly curved, with a power zone 190 approachingreading zone 120 being slightly farther apart and curved somewhatdownward. Note that FIG. 5 portrays incremental surface power (added tothe spherical surface) derived by computing mean power from differentialgeometry, not from loci of constant power based upon best acuity. Powerderived from differential geometry is simply the power computed as theaverage of the two principal curvatures. It is, in effect, the poweraverage of the astigmatic contours of the surface. This interpretationallows one only to portray power and astigmatism. Other more complexsurface deformations may be present that would result in non-astigmaticaberration forms.

FIG. 6 is a contour interval-style plot of actual refracted power oflens 100. FIG. 6 represents refracted power computed by locating anoptimum focus for a systematic array of locations in surface coordinatesof lens 100. Optimum foci for different portions of lens 100 have beencomputed by tracing large numbers of rays through those portions of lens100. The computed focal locations were then used to determine the actualrefracted power, taking into account contributions from all aberrationforms. Shapes of zones of constant refracted power 210 are discerniblydifferent from those power zones 180 of FIG. 5, particularly in theareas having relatively high refracted power, e.g., below MRP 140. Minordetails and differences in the curve shapes computed by surface geometryand refraction are not terribly consequential, as they can, in the caseof the refracted imagery model, be dependent upon the sampling intervalfor the display. For example, a refracted power value of 1.124 dioptermight be displayed as 1.0 diopter, whereas a value of 1.126 dioptermight be displayed as 1.25 diopter. It should also be noted that theshapes of these contours would be incrementally, but significantly,different if computed for a pupil diameter different from 3.5 mm.

With reference to FIG. 6, consider a vertical line 240 through acorridor on lens 100. Vertical line 240 includes reference points 260,262, 264, 266, 268, 270, 272 and 274. Table 2 lists vertical locationson the lens and a refracted power for each of these points. For example,point 274 is at a vertical location designated as +12 cm, and has arefracted power of 0.25 diopter. Thus, lens 100 has a refracted powerthat progresses from a first refracted power, i.e., 0.25 diopter, atpoint 274 in the corridor to a second refracted power, i.e. 2.0diopters, at point 260 in the corridor, in a vertical direction of about28 mm from point 274.

TABLE 1 Vertical Refracted Reference Location Power Point (millimeters)(diopter) 274 +12 0.25 272 +6 0.50 270 +2 0.75 268 −1 1.0 266 −4 1.25264 −7 1.50 262 −10 1.75 260 −16 2.00

FIG. 7 is a graphic representation of the data in TABLE 1 depicting therate of progression of refracted power in the surface of a 2.0 diopterlens. Consider a zone extending from point 270 to point 262. This zonehas a length of about 12 mm and includes all powers required for viewingobjects at intermediate distances, e.g., distances of about 55 cm toabout 135 cm. Refracted power progresses in the zone from a firstrefracted power at the top of the zone, point 270, through the refractedpowers at points 268, 266, and 264 to the refracted power at the bottomof point 262. Note that refracted power progresses linearly from anypoint to any other point in the zone. Note also that the rates of changefrom each end of the zone, i.e., from point 270 to point 272 and frompoint 262 to point 260, are slightly slower than the rate of change inthe zone, and the rate of change from point 272 to point 274 isidentical to the rate of change from point 262 to point 260. The averagerate of power change from the top of the corridor, point 274, to thebottom of the corridor, point 260, is 0.0625 diopter per millimeterwhich provides a smooth uninterrupted transition from one power toanother.

FIG. 8 is a contour interval-style plot of incremental surfaceastigmatism of lens 100. FIG. 8 illustrates a distribution ofastigmatism, expressed in diopter, calculated from differential surfacegeometry. Heavy contour lines occur at intervals of 0.5 diopter, andlight contour lines, separating the heavy contour lines, representastigmatism intervals of 0.25 diopter. Note that for lens 100,astigmatism content is less than 0.5 diopter inside a zone 220 centeredabout a meridian 230 through a center 280 of the Zernike coordinatesystem depicted in FIG. 1. Note that a corridor defined by the contourintervals of 0.5 astigmatism has a width greater than or equal to about6 millimeters along its length. Note also that a corridor defined by thecontour intervals of 1.0 diopter astigmatism has a width greater than orequal to about 15 millimeters.

FIG. 9 is a topographic map of image quality, based upon raytracecalculations, throughout a 2.0 diopter lens. Image quality is expressedin radians. Under normal conditions (lighting, object field contrast,chromatic content, etc.), the functional acuity threshold of the humanvisual system is 2-3 arc minute, or about 0.0006 to 0.0009 radians.Angular blur radius portrays the fidelity with which a point object isfocused. Under average lighting and contrast conditions, the averagehuman eye will resolve detail of the order of about 0.0005 radians.Thus, lens 100 is designed to have a refracted RMS angular blur radiusless than or equal to about 0.0005 radians in the corridor. FIG. 9 showscontours of blur sizes expressed in radians, and these contours create asomewhat different picture of lens performance, compared to theastigmatism map of FIG. 8. Given that 20-20 vision corresponds to athreshold resolution limit of about 1 arc minute, which is onlyachievable in ideal contrast conditions, and that this corresponds toabout 0.0003 radian, excellent acuity should be possible with lens 100over a corridor 250 having a width of greater than or equal to about 10mm along its length. If the pupil diameter were to be reduced below 3.5mm, visual acuity would be limited only by the eye itself over acorridor 255 as wide as 20 mm.

FIG. 10 is a composite plot that superimposes some of the surfaceastigmatism information of FIG. 8 upon the surface power information ofFIG. 5. Zone 290 is an area of high acuity implied by the 0.5 diopterastigmatism zone overlayed upon the lens 100 surface power contourintervals. However, zone 290 represents only a construct based upondifferential surface geometry, not addressing the effects of pupildiameter.

Assume a horizontal line 292 through zone 290 that includes a point 291on a left side of zone 290 and a point 293 on a right side of zone 290.At point 291, surface power is about 2.0 diopters, and at point 293,surface power is about 1.95 diopters. Thus, power varies alonghorizontal line 292 by about 0.05 diopter (i.e., 0.05=2.0−1.95).Generally, for any line across zone 290 in a horizontal direction, powervaries from a constant value, e.g., 2.0 diopters, by less than or equalto about 0.075 diopter. Note also, that the power extends in thehorizontal direction beyond the sides of zone 290. Lens 100 hasincremental surface power that varies from a constant value by less thanor equal to about 0.075 diopter in a horizontal direction over a widthgreater than or equal to about 10 millimeters that includes corridor 220(see FIG. 8).

FIG. 11 is a composite plot that superimposes some of the refracted RMSangular blur radius information of FIG. 9 upon the refracted powerinformation of FIG. 6. Zone 295 is an area of high acuity which takesinto account aberration products present in a 3.5 mm diameter pupil ,andwhich is implied by the RMS blur radius zone of less than 0.0005 radianin FIG. 9. Note that, while zone 295 roughly resembles zone 290 of FIG.10, there are qualitative and quantitative differences. The powercontours are uniformly spaced, but very slightly curved in zone 295.More particularly, zone 295 is wider than zone 290, based uponcalculations for a 3.5 mm diameter pupil. Had the design been createdfor a different pupil size, zone 295 would be differently-shaped, andits width and area different also.

Although several polymeric materials are candidates for implementationof lens 100, a preferred material for lens 100 is a polymeric materialknown as polycarbonate, having a nominal index of refraction of 1.5855at 587.6 nanometers. Lens 100 has a concave rear surface radius ofcurvature of 101 mm. Its front surface is convex, spaced at a vertexdistance of about 2.2 mm from the rear surface, and possesses a baseradius of 103 mm. Lens 100 has a form that is referred to as a weakpositive meniscus.

FIG. 12 is an illustration of an item of eyewear, i.e., glasses 900.Glasses 900 includes a frame 920 in which a lens 910 and a lens 930 aresituated. Glasses 900 may or may not include rims 915 and 925. Lenses910 and 930 are each molded to a specific predetermined shape and aspecific predetermined size, and fitted into frame 920 without edging.

Lenses 910 and 930 are similar to lens 100, but being designed andmanufactured for a right eye and left eye. When a person is wearingframe 920, the corridor of lens 910 is situated in front of the person'sright pupil 905, and the corridor of lens 930 is situated in front ofthe person's left pupil 935.

The relative positioning of lenses 910 and 930 satisfies a span ofinterpupillary distances of at least 6. For example, glasses 900, i.e.,a single pair of glasses, could satisfy both an interpupillary distanceof 57 mm and an interpupillary distance of 63 mm.

For each lens described herein, the design of the lens can be conveyedon or in a tangible medium such as a paper or computer-readable storagedevice (e.g., compact disk or electronic memory). For example, where thedesigning includes representing a surface of the lens by way of aZernike expansion, the Zernike expansion, and thus the design, can beconveyed on the paper or in the computer-readable storage device. Also,any of the lenses described herein can be configured as a progressiveaddition lens.

It should be understood that various alternatives and modifications ofthe present invention could be devised by those skilled in the art. Thepresent invention is intended to embrace all such alternatives,modifications and variances that fall within the scope of the appendedclaims.

What is claimed is:
 1. An item of eyewear, comprising: a lens holder;and a pair of progressive addition lenses situated in said lens holderto satisfy a span of interpupillary distances of at least 6 millimeters.2. A method comprising: representing a surface for each of a pair ofophthalmic lenses by way of a Zernike expansion; and situating said pairof lenses in a lens holder to satisfy a span of interpupillary distancesof at least 6 millimeters.
 3. The method of claim 2, wherein saidophthalmic lenses are progressive addition lenses.
 4. The method ofclaim 3, wherein said ophthalmic lenses are aspheric lenses.
 5. A methodcomprising: designing an ophthalmic lens, wherein said designingemploys, as design parameters, (a) a predetermined boundary shape ofsaid ophthalmic lens for ultimate use, and (b) a predetermined boundarysize of said ophthalmic lens for ultimate use.
 6. The method of claim 5,wherein said ophthalmic lens is a progressive addition lens.
 7. Themethod of claim 5, wherein said ophthalmic lens is an aspheric lens. 8.The method of claim 5, wherein said designing comprises representing asurface of said ophthalmic lens by way of a Zernike expansion.
 9. Themethod of claim 8, wherein said Zernike expansion employs at least tenterms.
 10. The method of claim 5, wherein said designing employs, as adesign parameter, a pupil size of a wearer for use of said ophthalmiclens.
 11. The method of claim 5, further comprising manufacturing saidophthalmic lens.
 12. The method of claim 11, further comprisingsituating said ophthalmic lens in a lens holder.
 13. The method of claim5, wherein said ophthalmic lens is one of two such lenses that whensituated in a lens holder satisfy a span of interpupillary distances ofat least 6 millimeters.